Brighton had an opportunity to reply immediately, but Murphy kept out Mackail-Smith's shot from 12 yards.
Mclean, 26, has formed a consistent partnership with Craig Mackail-Smith but Wright has impressed in pre-season.
Brighton's Craig Mackail-Smith almost replied late on but his header was kept out by goalkeeper Joe Murphy.
Mackail-Smith is yet to kick a ball in pre-season following a recurrence of his body alignment problems.
And it should have been a much greater margin, with Mackail-Smith and Aaron McLean both hitting the bar.
Craig Mackail-Smith, Joe Lewis, Aaron Mclean and Lee Frecklington have each been linked with moves away from London Road.
Peterborough should have won by many more in truth, with Dean Keates, Mackail-Smith and Boyd himself all going close.
Mackail-Smith's body alignment issues put pressure on his hips, resulting in periodic niggles such as his current groin problem.
Aside from Mackail-Smith and Keates, Ferguson named a mostly second string side which included transfer-listed Sergio Torres and Danny Blanchett.
Mackail-Smith has been struggling with an injury relating to his body alignment problems and has barely trained since returning for pre-season.
Craig Mackail-Smith put the hosts ahead early on with a sharp header before Tom Williams made it two from 18 yards.
The Posh boss also confirmed that he has still yet to receive an approach for Mclean and Mackail-Smith or winger George Boyd.
Posh are facing an injury crisis with George Boyd and Craig Mackail-Smith both severe doubts and Exodus Geohaghon and Gabby Zakuani already ruled out.
But the Posh's pre-match preparations were not helped by the loss of strike trio Aaron McLean, George Boyd and Craig Mackail-Smith to a virus.
Zakuani is still struggling with a groin strain, while Geohaghon has a hamstring problem, Mackail-Smith has picked up a virus and Boyd has an ankle problem.
Wright is currently the club's third choice striker behind Aaron Mclean and Craig Mackail-Smith, and admits he faces a battle to win a regular place in the side.
Posh cruised into the fourth round with goals from Craig Mackail-Smith and Tommy Williams crowning a dominant performance as they pummelled a youthful Newcastle side from start to finish.
Posh already have three proven strikers on their books in the shape of Aaron Mclean, Craig Mackail-Smith and new signing Dave Hibbert, so will not be desperate to bolster their attacking options.
McLean had already hit the bar with a powerful drive before some poor defending allowed Mackail-Smith to make the most of a deflection in the Newcastle area and head in from six yards.
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